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arXiv · 1501.05889

On the equivalence between continuum and car-following models of traffic flow

Wen-Long Jin
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Abstract

Recently different formulations of the first-order Lighthill-Whitham-Richards (LWR) model have been identified in different coordinates and state variables. However, there exists no systematic method to convert higher-order continuum models into car-following models and vice versa. In this study we propose a simple method to enable systematic conversions between higher-order continuum and car-following models in two steps: equivalent transformations of variables between Eulerian and Lagrangian coordinates, and finite difference approximations of first-order derivatives in Lagrangian coordinates. With the method, we derive higher-order continuum models from a number of well-known car-following models. We also derive car-following models from higher-order continuum models. For general second-order models, we demonstrate that the car-following and continuum formulations share the same fundamental diagram, but the string stability condition of a car-following model is different from the linear stability condition of a continuum model. This study reveals relationships between many existing models and also leads to a number of new models.

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Wen-Long Jin. 2014-12-02. On the equivalence between continuum and car-following models of traffic flow. https://arxiv.org/abs/1501.05889

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